Question

Elena has a boat that would go 9 miles per hour in still water. She travels downstream for a certain distance and then back upstream to where she started. Elena notices that it takes her 4 hours to travel upstream and 2 hours to travel downstream.

The river’s speed is r miles per hour. Write an equation that will help her solve for r. Don't simplify anything, just give the initial equation.
(Hint: Use distance = rate x time for each direction on the river)

Answer 1

The equation that Elena can use to solve for the river's speed r is (9 + r) * 2 = (9 - r) * 4, which is derived from the formula distance = rate x time for each direction on the river.

Step-by-step explanation:

Elena has a boat that can travel at a speed of 9 miles per hour in still water. While traveling downstream, the speed of the boat will be the sum of its own speed in still water and the river's speed. While traveling upstream, the speed of the boat will be its speed in still water minus the river's speed. Therefore, using the formula distance = rate x time, we can write two equations for the distances traveled downstream and upstream, which should be equal:

• Downstream Distance: (9 + r) * 2
• Upstream Distance: (9 - r) * 4

Since Elena travels the same distance downstream and then back upstream to her starting point, these two distances are equal. Hence, the equation to find the river's speed r is:

(9 + r) * 2 = (9 - r) * 4